Endless lego set

The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. They noticed that a 7 kg structure could not build them. Others do. Finally, they decided to find out from what least weight they already know, using 6, 9 and 20 kilograms, to build each building. What is the smallest weight of the building from which all the heavier buildings can be built?

Correct answer:

m =  44 kg

Step-by-step explanation:

6=23 9=32 20=225 LCM(6,9,20)=22325=180  m1=LCM(6,9,20)=180 m=2 3 a+3 3 b+2 2 5 c m=2 (3a+2 5c)+3 3b 44=22 11 m=44 kg

We will be pleased if You send us any improvements to this math problem. Thank you!


Tips to related online calculators
Do you solve Diofant problems and looking for a calculator of Diofant integer equations?
Do you want to perform natural numbers division - find the quotient and remainder?

We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions:

  • Z9-I-4
    numbers_30 Kate thought a five-digit integer. She wrote the sum of this number and its half at the first line to the workbook. On the second line wrote a total of this number and its one fifth. On the third row, she wrote a sum of this number and its one nines. Fina
  • Bent scale
    vaha_1 Monica weighed 52 kg. Sara 54 kg. Together they weighed 111 kg. They noticed that the weight on the scale was bent. How much did they really weigh?
  • The bakery
    chlieb The bakery delivered 60 kg of bread to the store, the breads weighed 1 kg and 2 kg, a total of 35 pieces. How many loaves weighed 1 kg and how many were two-kilo loaves?
  • Diofant equation
    diofantos In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
  • Center of gravity
    map_1 The mass points are distributed in space as follows - specify by coordinates and weight. Find the center of gravity of the mass points system: A1 [1; -20; 3] m1 = 46 kg A2 [-20; 2; 9] m2 = 81 kg A3 [9
  • Diofant 2
    1diofantos Is equation ? solvable on the set of integers Z?
  • Blood
    krv In the human body, the blood is about 7.3% body weight. How many kilograms of blood are in the human body with weight 109 kg?
  • Ratio
    maliny Alena collected 7.8 kg of blueberries, 2.6 kg of blackberries, and 3.9 kg of cranberries. Express the ratio in the smallest natural numbers in this order.
  • The piglet
    piglet The weight of the piglet regularly grew by five kilograms for four months. Determine the proportion by weight of the piglet in each month if the first weighed 35 kg.
  • Minimum surface
    cuboid_20 Find the length, breadth, and height of the cuboid-shaped box with a minimum surface area, into which 50 cuboid-shaped blocks, each with length, breadth, and height equal to 4 cm, 3 cm, and 2 cm respectively, can be packed.
  • Barrel 4
    sudy Barrel of water weighs 63 kg. After off 75% water, the weight of the barrel with water is 21 kg. How many kg weigh empty barrel and how many kgs water in it?
  • The devils
    cert The devils weighed in hell with Dorota. They found that Dorota and the two devils weigh 250 kg together, and Dorota and the four devils weigh 426 kg. All the devils weigh the same. How Much Does Dorota Weigh?
  • Seawater
    ice_cubes Seawater has a density of 1025 kg/m3, ice 920 kg/m3. 8 liters of seawater froze and created a cube. Calculate the size of the cube edge.
  • Bags
    kufor The first bag has a weight of 18 kg, the second bag is a one-third lighter than the first and the third bag has three times less the weight of all three bags together. Determine their weights.
  • Barrel 3
    sud-s-vodou Barrel with water has a weight 118 kg. When we get off 75% of water it has a weight 35 kg. How many kg has empty barrel?
  • Eiffel Tower
    eiffel_tower Eiffel Tower in Paris is 300 meters high and is made of steel. Its weight is 8000 tons. How tall is the tower model made ​​of the same material if it weighs is 2.4 kg?
  • Diofant equation
    eq222_19 250x + 120y = 5640